A widely used principle for learning a predictor map is empirical risk minimization (ERM).
The idea of ERM is to learn a predictor map with small training error [1]}, [2]}, [3]}
\(\mathcal {E} :=(1/|\mathcal {T}|) \sum _{(\mathbf {x},y) \in \mathcal {T}} \mathcal {L}(g,(\mathbf {x},y)).\) 
